The relative speed of a train in respect of a car is 90 km/h when train and car are moving opposite to each other. Find the actual speed of train, if car is moving with a speed of 15 km/h.

Options

A. a. 80 km/h
B. b. 105 km/h
C. c. 75 km/h
D. d. 100 km/h

Answer

To solve the problem, we need to find the actual speed of the train given the relative speed between the train and the car when they are moving in opposite directions.

### Step-by-Step Solution:

1. **Understand the Concept of Relative Speed:**
When two objects are moving in opposite directions, their relative speed is the sum of their individual speeds.
\[ \text{Relative Speed} = \text{Speed of Train} + \text{Speed of Car} \]

2. **Identify Given Values:**
- Relative Speed = 90 km/h
- Speed of Car = 15 km/h

3. **Set Up the Equation:**
Using the formula for relative speed, we can express the speed of the train (let's denote it as \( S_t \)):
\[ S_t + 15 = 90 \]

4. **Solve for the Speed of the Train:**
To find the speed of the train, we can rearrange the equation:
\[ S_t = 90 - 15 \]
\[ S_t = 75 \text{ km/h} \]

5. **Conclusion:**
The actual speed of the train is 75 km/h.